Figure REF  shows the optimal level of precision \(n^*\)  when varying the number of local iterations \(I\) . We use the same CNN architecture in Fig. REF . We can observe that \(n^*\)  increases with \(I\) . This is because, as \(I\)  increases, the local models converge to the local optimal faster as SGD averages out the effect of quantization error [1]}. Hence, a lower \(n\)  can be chosen by leveraging the increased \(I\)  to minimize the total energy consumption. We can observe that only \(n= 7\)  is required at \(I= 20\)  while we need \(n= 10\)  at \(I= 3\) .
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